Farmer Joe owns a cow, a goat, and a sheep. The animals each eat grass at a constant rate, and the grass grows at a constant rate. And Farmer Joe occasionally lets them eat the grass on a small pasture of his.

• If the cow and the goat graze together, the pasture is bare after 45 days.
• If the cow and the sheep graze together, the pasture is bare after 60 days.
• If the cow grazes alone, the pasture is bare after 90 days.
• If the goat and the sheep graze together, the pasture is bare after 90 days, also.

How long will it take for the pasture to be bare if all three animals graze together?

(In reply to Solution by Larry)

Now that you mention it, I suppose that I didn't need the fourth statement either.  Right after solving for the goat's eating rate, I could have just added it to the total eating rate in statement two.

BTW, to Ravi, yes, that's why I make assumptions--to find the likely intended solution.  The "No solution yet" refers to the "official" solution, usually written by the author of the puzzle.  It doesn't refer to the solutions in the comments.

Posted by Tristan on 2004-10-15 07:06:05